Strip!

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Children and scientists alike are fascinated by the Möbius strip. The mysterious three-dimensional structure is formed physically and mathematically when a ribbon is twisted through 180 degrees and its two ends joined together. Trace a pencil from one point on the ribbon and it soon reaches the starting point without you having to lift the pencil off to change sides.

They are simple to make with paper and sticky tape, but physicists have now found a way to crystallise a Möbius strip.

Satoshi Tanda at Hokkaido University in Japan, and colleagues, have demonstrated that crystals - ordinarily neat and ordered gatherings of atoms, ions, or molecules - can easily be grown in strips. So far commonplace, but the Japanese team have added a twist. A solid crystal, one might think, should not be able to take on the bends of a Möbius. But, the researchers have grown crystals of niobium and selenium on a droplet of liquid selenium to show that the children's favourite can be grown in a crystal garden.

The growing crystal NbSe₃ (niobium triselenide) crystal gradually works its way around the drop of selenium ultimately forming a seamless ring. The team can then remove the crystalline ring completely from the drop to reveal a tiny structure the diameter of a human hair.

By tweaking the growing conditions, the researchers say they can coax the growing ring-crystals to twist and form more than a simple belt around the drop, producing a molecular Möbius strip. The spherical droplet acts as a spool, explains Tanda, "This technique could be extended to a wide range of materials, and we have already obtained topological variants of tantalum compounds with selenium and sulphur."

Theoretically, such structures might be useful in studying the minutiae of quantum mechanics. The spin on an electron, for instance, which takes two full "turns" to come back to its starting point. The technique might also be used to template the growth of complex molecular structures with novel architecture and chirality.

Nature, 2002, 417, 397-398^*

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